Knowledge that Transforms

We present an approach to network formation based on the notion that social networks are formed by individual decisions that trade off the costs of forming and maintaining links against the potential rewards from doing so. We suppose that a link with another agent allows access, in part and in due course, to the benefits available to the latter via his own links. Thus individual links generate externalities whose value depends on the level of decay/delay associated with indirect links. A distinctive aspect of our approach is that the costs of link formation are incurred only by the person who initiates the link. This allows us to formulate the network formation process as a noncooperative game. We first provide a characterization of the architecture of equilibrium networks. We then study the dynamics of network formation. We find that individual efforts to access benefits offered by others lead, rapidly, to the emergence of an equilibrium social network, under a variety of circumstances. The limiting networks have simple architectures, e.g., the wheel, the star, or generalizations of these networks. In many cases, such networks are also socially efficient.

This paper examines an employment relation in which individual workers enjoy some bargaining power vis-a-vis the firm although they are not unionized. The main elements of the situations studied here are that the employment contracts are non-binding across periods of production and that the firm has opportunities to replace workers. The paper analyzes a dynamic model in which the processes of contracting and recontracting between the firm and its workers are intertwined with the dynamic evolution of the firm's workforce. The analysis of the model is somewhat complicated because the employment level is a nondegenerate state variable that evolves over time and is affected by past decisions. The main analytical results characterize certain important equilibria: the profit maximizing and stationa˙ry equilibria. The unique stationary equilibrium is markedly inefficient: it exhibits inefficient over-employment and the steady state wages coincide with the workers' reservation wage. It confirms earlier results derived by Stole and Zwiebel (1996a,b) in the context of a static model and shows that they are very robust even when the firm has nearly frictionless hiring opportunities. In contrast, in the profit maximizing equilibrium the outcome is nearly efficient and the wage exhibits a mark-up over the reservation wage.

We propose a simple adaptive procedure for playing a game. In this procedure, players depart from their current play with probabilities that are proportional to measures of regret for not having used other strategies (these measures are updated every period). It is shown that our adaptive procedure guaranties that with probability one, the sample distributions of play converge to the set of correlated equilibria of the game. To compute these regret measures, a player needs to know his payoff function and the history of play. We also offer a variation where every player knows only his own realized payoff history (but not his payoff function).

This paper studies the monotonicity of individual and market demand with the aid of the indirect utility function. We identify sufficient (and in a sense, necessary) conditions on an agent's indirect utility which will guarantee that he has a monotonic demand function. Our conditions also point to a natural way of extending the result of Hildenbrand (1983). Hildenbrand showed that market demand is monontonic if the income distribution has a downward sloping density, even though individual agents' demand function might violate monotonicity. Using the indirect utility function, we introduce a measure of violations of individual monotonicity that allows us to identify a larger class of density functions that will generate a monotonic market demand.

This paper develops an asymptotic theory for time series binary choice models with nonstationary explanatory variables generated as integrated processes. Both logit and probit models are covered. The maximum likelihood (ML) estimator is consistent but a new phenomenon arises in its limit distribution theory. The estimator consists of a mixture of two components, one of which is parallel to and the other orthogonal to the direction of the true parameter vector, with the latter being the principal component. The ML estimator is shown to converge at a rate of n3/4 along its principal component but has the slower rate of n1/4 convergence in all other directions. This is the first instance known to the authors of multiple convergence rates in models where the regressors have the same (full rank) stochastic order and where the parameters appear in linear forms of these regressors. It is a consequence of the fact that the estimating equations involve nonlinear integrable transformations of linear forms of integrated processes as well as polynomials in these processes, and the asymptotic behavior of these elements is quite different. The limit distribution of the ML estimator is derived and is shown to be a mixture of two mixed normal distributions with mixing variates that are dependent upon Brownian local time as well as Brownian motion. It is further shown that the sample proportion of binary choices follows an arc sine law and therefore spends most of its time in the neighborhood of zero or unity. The result has implications for policy decision making that involves binary choices and where the decisions depend on economic fundamentals that involve stochastic trends. Our limit theory shows that, in such conditions, policy is likely to manifest streams of little intervention or intensive intervention.

.The paper develops a reputation based theory of bargaining. The idea is to investigate and highlight the influence of bargaining ‘‘postures’’ on bargaining outcomes. A complete information bargaining model a la Rubinstein is amended to accommodate ‘‘irrational ` types’’ who are obstinate, and indeed for tractability assumed to be completely inflexible in their offers and demands. A strong ‘‘independence of procedures’’ result is derived: after initial postures have been adopted, the bargaining outcome is independent of the fine details of the bargaining protocol so long as both players have the opportunity to make offers frequently. The latter analysis yields a unique continuous-time limit with a war of attrition structure. In the continuous-time game, equilibrium is unique, and entails delay, consequently inefficiency. The equilibrium outcome reflects the combined influence of the rates of time preference of the players and the ex ante probabilities of different irrational types. As the probability of irrationality goes to zero, delay and inefficiency disappear; furthermore, if there is a rich set of types for both agents, the limit equilibrium payoffs are inversely proportional to their rates of time preference.

This paper examines the abilities of learning models to describe subject behavior in experiments. A new experiment involving multistage asymmetric-information games is conducted, and the experimental data are compared with the predictions of Nash equilibrium and two types of learning model: a reinforcement-based model similar to that used by Roth and Erev (1995), and belief-based models similar to the ‘cautious fictitious play’ of Fudenberg and Levine (1995, 1998) These models make predictions that are qualitatively similar cycling around the Nash equilibrium that is much more apparent than movement toward it. While subject behavior is not adequately described by Nash equilibrium, it is consistent with the qualitative predictions of the learning models. We examine several criteria for quantitatively comparing the predictions of alternative models. According to almost all of these criteria, both types of learning model outperform Nash equilibrium. According to some criteria, the reinforcement-based model performs better than any version of the belief-based model; according to others, there exist versions of the belief-based model that outperform the reinforcement-based model. The abilities of these models are further tested with respect to the results of other published experiments. The relative performance of the two learning models depends on the experiment, and varies according to which criterion of success is used. Again, both models perform better than equilibrium in most cases.